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Wednesday, February 11, 2009

The problem with regression betas

I must confess that I find the practices used to estimate betas to be both sloppy and counter intuitive. The standard approach, offered in every finance text book, is to regress returns on the stock against returns on a market index, with the slope yielding the beta. I have five problems with this approach:

1. Statistically, the slope coefficient in a simple regression comes with a standard error. The beta estimate for a typical US company has a standard error that is about 0.20. One way to read this number, is when you are told that the beta for a company (from a regression) is 1.10, the true beta could be anywhere from 0.70 to 1.50 (plus or minus two standard errors).

2. Outside the US, regression betas often look much more precise but only because the indices used tend to be narrow local indices (DAX, Bovespa, Sensex). As anyone who has toyed with the parameters of the beta regression (2 vs 5 years, daily vs weekly, different market indices) knows, you can arrive at very different betas for the same company, based on your choices. None of them is the right beta, and they may all be coming from the same distribution, but it is a wide one.

3. By definition, a regression beta has to be backward looking, since you need past returns. To the extent that companies change their business mixes (by expanding, divesting and acquiring businesses) or their financial leverage (debt ratios) over time, the regression beta may not be a good measure of the beta for the future.

4. If the only way you can estimate betas is with a regression, you will be stymied right from the start, if you are analyzing the division of a company, a private business or a company that went public recently.

5. By making beta a statistical number, we are missing the fundamentals that drive beta. Every company has an intrinsic or true beta that comes from choices it has made and understanding how these choices can cause your beta to change is central to a better beta estimate.

So, I would take any beta reported for a company by a service or an analyst with a grain of salt. It probably came from a regression and should not define your thinking about the firm's risk. In my next two posts, I will offer my analysis of the determinants of betas and an alternative to regression betas.

13 comments:

Professor--This is not quite on point (I should have posted this when you were talking about ERP) but perhaps it is close enough for you to respond. In his book Venture Capital and the Finance of Innovation Prof Metrick notes that many emerging countries have betas of less than 1, when compared to a global stock index. He notes that Brazil, even though it has a market volatility more than 6 times that of the US, has a beta of less than 1 (at least as of the time of writing). Obviously, as he notes, this is because beta is driven by covariance and not variance. I wonder what you think of this approach and whether you think it is appropriate to assume take the perspective of an internationally diversified investor? The result of doing this is to get costs of equity for Brazil that are below that of the US. This makes me nervous and makes me think that I really don't have a clue!

It is true that regression beta is of little use and we can derive any beta by varying the length of time period. Calculating beta by pure play method is somewhat convincing however here too the main determinant which affects the beta to an greater extent is length of time period. I found an article What's Your Real Cost of Capital?Publication Date: Oct 1, 2002Author(s): James J. McNulty, Tony D. Yeh, William S. Schulze, Michael H. Lubatkin Type: Harvard Business Review Articlewhere they say that we should take stock options volatility to calculate beta as the volatility in options reflect the true analysis of available information of the company and what market feels about that company's policy. However here also the constraint is same that is length of time period. So I want to say that in your next article please do mention about the correct frame of time period and how to select a time period for calculating beta's for company stock. One more thing what should we do in case beta is negative?.Thanking you,Manish

I have seen the option based approaches. It is true that you can get a forward looking volatility from an option price, but volatility is not the determinant of betas. It is the correlation with the market and no option can give that information.Beta = Correl with mkt (Std dev of stock/ Std dev of market) What option based approaches provide is a measure of relative standard deviation and total risk. If that is what you want to capture, they work well. If not, they do not.

I have a question about the terminal growth rate. In my valuations i find that the terminal growth rate has great influence in my final results. What terminal growth rate do you use in your valuations? I personally use 3.4% Is this to low? I think 6% is way to high. Thanks

I wrote my master thesis in caclualting the cost of capital in emerging markets and i figured out that you have to make adjustments to the CAPM in these markets.

The Capital Asset Pricing Model (CAPM) has various criticisms even for using it in developed integrated markets, so applying this model to calculate the cost of equity, and therefore cost of capital, in emerging and semi-integrated markets should have even more flaws, because assumptions of the Capital Asset Pricing Model (CAPM) like that capital markets have perfect information and are perfectly correlated are violated in these markets.For this reason there are different models that try to correct these flaws by doing an extension of the CAPM or even proposing non-CAPM models.

Some of the models I learnd about and exposed on my thesis are the Global CAPM, the Local CAPM, the Baekert-Harvey Micture Model, the adjusted local campm variant, the adjusted hybrid CAPM variant, the Damodaran model, where you adjust country risk by volatility the volatilities of the local equity markets and the volaitilty of the sovereign bond, Godfrey-Espinoza Model, the Estrada model (non-CAPM and one of my favourites) and the Erb-Harvey-Viskanta model.

All theses models are easy to find on the net. If you wouild like I can send you my thesis so you can check it out. I manily covers estimating the cost of capital in Argentina, Brazil, Chile and Mexico.